Grid-characteristic method with implicit schemes and contact conditions at the material interface

The paper presents a modified grid-characteristic method for modeling the propagation of elastic waves in heterogeneous media with explicit material boundaries. The proposed approach is based on the use of implicit and explicit numerical solution schemes, which together ensure stability and accuracy at large time steps and small space steps in areas with elongated shapes. The correct formulation of contact conditions between materials was implemented both in the form of reflected and refracted waves, and by modifying the lines of the system of equations for the implicit scheme. Numerical experiments for one-dimensional and two-dimensional problems, including wave modeling in multilayer structures and glass composites, are presented. The convergence order has been estimated for various schemes. The results show the possibility of the developed method to provide high modeling accuracy and the ability to describe complex wave patterns in heterogeneous media.